"Fillet" separates the whole object. My workaround is as follows: Create Fillet, then copy and Ctrl + Z.
Now reinsert and with the outer edges of the "filet" the entire object trimming.
Then together with "Boole Union" the fillets with the object.

This is very awkward, but at the moment seems not to be working differently.
If you want to try, may gladly do it.
You can see the critical area in my screenshot.

Hi Jörg , that's a bug in fillet where the fillet mechanism is having some problem finishing everything up correctly.

I've modified the fillet engine so in cases where it is not able to finish things 100% all the way it will still give back the stuff that it was able to do (instead of just doing nothing at all) so that you can have some possibility to do something with those pieces just like you did.

I just had the same experience today... After I Boolean Differenced a small object from an even larger one I went to Fillet a bunch of segments that were all on connected surfaces that had funny angles to each other - it worked, but the entire solid broke down into separate once-joined surfaces.
Okay, it was a joined surface that I had to reconstruct anyways and then no problem from the Fillet.